Question

solve the following equations (i)2x-3=7
(ii)2z+9=4
(iii)8-3x=-10
(iv)2x-3=x+2
(v)5x-3=3x+7​

Answer 1

Answer:

1.2x=7+3

x=10/2

x=5

2. 2z=9-4

2z=5

z=5/2

z=2.5

3.-3x=-10-8

-3x=-18

x=6

Answer 2

Answer i :-

$:\longmapsto\sf2x - 3 = 7$

Transposing 3 from LHS to RHS, changing it's sign,

$:\longmapsto\sf2x = 7 + 3$

Adding 3 to 7,

$:\longmapsto\sf2x = 10$

Transposing 2 from LHS to RHS, changing it's sign,

$:\longmapsto\sf x = \dfrac{10}{2}$

Dividing 10 by 2,

$:\longmapsto \underline{ \boxed{ \sf x = 5}}$

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Answer ii :-

$:\longmapsto\sf2z + 9 = 4$

Transposing 9 from LHS to RHS, changing its sign,

$:\longmapsto\sf2z = 4 - 9$

Subtracting 9 from 4,

$:\longmapsto\sf2z = - 5$

Transposing 2 from LHS to RHS, changing it's sign,

$:\longmapsto \underline{ \boxed{\sf z = \dfrac{ - 5}{ \: \: \: 2} }}$

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Answer iii :-

$:\longmapsto\sf8 - 3x = - 10$

Transposing 8 from LHS to RHS, changing it's sign,

$:\longmapsto\sf - 3x = - 10 - 8$

Subtracting 8 from -10,

$:\longmapsto \sf - 3x = - 18$

Transposing -3 from LHS to RHS, changing it's sign,

$:\longmapsto\sf x = \dfrac{ - 18}{ - 3}$

Dividing -18 by -3,

$:\longmapsto \underline{ \boxed{\sf x = 6}}$

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Answer iv :-

$:\longmapsto\sf2x - 3 = x + 2$

Putting the constant and variable terms on different sides by the method of transposition,

$:\longmapsto \sf2x - x = 2 + 3$

On simplifying,

$:\longmapsto \underline{ \boxed{ \sf x = 5}}$

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Answer v :-

$:\longmapsto\sf5x - 3 = 3x + 7$

Putting the constant and variable terms on different sides by the method of transposition,

$:\longmapsto\sf5x - 3x = 7 + 3$

On simplifying,

$:\longmapsto\sf2x = 10$

Transposing 2 from LHS to RHS, changing it's sign,

$:\longmapsto \sf x = \dfrac{10}{2}$

Dividing 10 by 2,

$:\longmapsto \underline{ \boxed{\sf x = 5}}$